Solve 1/2x+1>x-1

$$\frac { 1 } { 2 } x + 1 > x - 1$$

Solve for x

$$x<4$$

Solution Steps

Subtract x from both sides.

$$\frac{1}{2}x+1-x>-1$$

Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.

$$-\frac{1}{2}x+1>-1$$

Subtract 1 from both sides.

$$-\frac{1}{2}x>-1-1$$

Subtract 1 from -1 to get -2.

$$-\frac{1}{2}x>-2$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.

$$x<-2\left(-2\right)$$

Multiply -2 and -2 to get 4.

$$x<4$$